- Ohm: It is the S.I. unit of resistance. A conductor has a resistance of one ohm if a current of one ampere flows through it on applying a potential difference of one volt across its ends. 1 ohm = 1 volt/1 ampere or 1Ω = 1V/1A
- Factors on which resistance of a conductor depends: The resistance R of a conductor depends
i) Directly on its length L i.e. R α L. ii) inversely on its area of cross-section A i.e. R α 1/A iii) on the nature of material of the conductor on. On combining the above factors, we get R α L/A R = ρ * L/A The proportionality constant ρ is called
resistivity of conductor.
- Resistivity: It is defined as the resistance offered by a cube of a material of side 1 m when current flows perpendicular to its opposite faces. Its S.I. unit is ohm-meter (Ωm). Resistivity, ρ = RA/L
- Equivalent resistance: If a single resistance can replace the combination of resistances in such a manner that the current in the circuit remains unchanged, then that single resistance is called the equivalent resistance.
- Laws of resistances in series: i) Current through each resistance is same. ii) Total voltage across the combination = Sum of the voltage drops. V= V1 + V2 + V3 iii) Voltage drops across any resistor is proportional to its resistance. V1 = IR1, V2 = IR2, V3 = IR3 iv) Equivalent resistance = Sum of the individual resistances. Rs = R1 + R2 + R3 v) Equivalent resistance is larger than the largest individual resistance.
- Laws of resistances in parallel: i) Voltage across each resistance is same and is equal to the applied voltage. ii) Total current = Sum of the currents through the individual resistances. I = I1 + I2 + I3 iii) Currents through various resistances are inversely proportional to the individual resistances. I1 = V/R1, I2 = V/R2, I3 = V/R3 iv) Reciprocal of equivalent resistance = Sum of reciprocals of individual resistances. 1/Rp = 1/R1 + 1/R2 + 1/R3 v) Equivalent resistance is less than the smallest individual resistance.
- Joule’s law of heating: It states that the heat produced in a conductor is directly proportional to (i) the square of the current I through it (ii) proportional to its resistances R and (iii) the time t for which current is passed. Mathematically, it can be expressed as H = I2Rt joule = I2Rt/4.18 cal or H = VIt joule = VIt/4.18cal
- Electric energy: It is the total work done in maintaining an electric current in an electric circuit for given time.
Electric energy, W = VIt = I2Rt joule
- Electrical power: Electrical power is the rate at which electric energy is consumed by an appliance.
P = W/t = VI = I2R = V2/R
- Watt: It is the S.I. unit of power. The power of an appliance is 1 watt if one ampere of current flows through it on applying a potential differences of 1 volt across its ends. 1 watt = 1 joule/1 second =1 volt x 1 ampere or 1 W = 1 Js-1 = 1 VA 1 kilowatt = 1000 W 1Mega watt= 106 watt 1Gigawatt=109 watt
- Kilowatt hour: It is the commercial unit of electrical energy. One kilowatt hour is the electric energy consumed by an appliance of 1000 watts when used for one hour. 1 kilowatt hour (kWh) = 3.6 x 106 J